Thank you for this very helpful reply. I'm afraid that I'm not convinced by the proof for the case n = 2 on the other thread. I suppose I could try to fill in the details but I do this type of maths for enjoyment, and I enjoy the process of reading through complete proofs more than I enjoy working out the details.So what are these missing details I'm referring to? The answer is that it doesn't seem at all transparent to me that, in the infinite case, almost all the horses get matched at some finite stage. (The finite case is fine).